Final answer:
The exponential equation 4^(2x + 3) = 1 can be solved by equating 2x + 3 to 0 since any base raised to the power of 0 equals 1. Subtracting 3 from both sides and then dividing by 2 yields the solution x = -3/2.
Step-by-step explanation:
The question asks us to solve an exponential equation that does not require the use of logarithms: 4^(2x + 3) = 1. To solve this, we can make use of the property that any non-zero number raised to the power of 0 is equal to 1, i.e., b^0 = 1. Since 1 can be written as 4^0, we can deduce that 2x + 3 must be equal to 0 for the equation to hold true.
Thus, we have 2x + 3 = 0. To find x, we subtract 3 from both sides and then divide by 2. This gives us:
- 2x + 3 - 3 = 0 - 3
- 2x = -3
- x = -3 / 2
So, the solution to the equation 4^(2x + 3) = 1 is x = -3/2.